scout: Covariance-regularized regression, aka the Scout.

Description

The main function of the "scout" package. Performs covariance-regularized regression. Required inputs are an x matrix of features (the columns are the features) and a y vector of observations. By default, Scout(2,1) is performed; however, $p_1$ and $p_2$ can be specified (in which case Scout($p_1$, $p_2$) is performed). Also, by default Scout is performed over a grid of lambda1 and lambda2 values, but a different grid of values (or individual values, rather than an entire grid) can be specified.

Usage

scout(x,y,newx,p1=2,p2=1,lam1s=seq(.001,.2,len=10),lam2s=seq(.001,.2,len=10), rescale=TRUE, trace=TRUE,standardize=TRUE)

Arguments

A matrix of predictors, where the rows are the samples and the columns are the predictors

A matrix of observations, where length(y) should equal nrow(x)

newx

An *optional* argument, consisting of a matrix with ncol(x) columns, at which one wishes to make predictions for each (lam1,lam2) pair.

The $L_p$ penalty for the covariance regularization. Must be one of 1, 2, or NULL. NULL corresponds to no covariance regularization. WARNING: When p1=1, and ncol(x)>500, Scout can be SLOW. We recommend that for very large data sets, you use Scout with p1=2. Also, when ncol(x)>nrow(x) and p1=1, then very small values of lambda1 (lambda1 < 1e-4) will cause problems with graphical lasso, and so those values will be automatically increased to 1e-4.

The $L_p$ penalty for the estimation of the regression coefficients based on the regularized covariance matrix. Must be one of 1 (for $L_1$ regularization) or NULL (for no regularization).

lam1s

The (vector of) tuning parameters for regularization of the covariance matrix. Can be NULL if p1=NULL, since then no covariance regularization is taking place. If p1=1 and nrow(x)500 then we really do not recommend using p1=1, as graphical lasso can be uncomfortably slow.

lam2s

The (vector of) tuning parameters for the $L_1$ regularization of the regression coefficients, using the regularized covariance matrix. Can be NULL if p2=NULL. (If p2=NULL, then non-zero lam2s have no effect). A value of 0 will result in no regularization.

rescale

Should coefficients beta obtained by covariance-regularized regression be re-scaled by a constant, given by regressing $y$ onto $x beta$? This is done in Witten and Tibshirani (2008) and is important for good performance. Default is TRUE.

trace

Print out progress? Prints out each time a lambda1 is completed. This is a good idea, especially when ncol(x) is large.

standardize

Should the columns of x be scaled to have standard deviation 1, and should y be scaled to have standard deviation 1, before covariance-regularized regression is performed? This affects the meaning of the penalties that are applied. In general, standardization should be performed. Default is TRUE.

Value

intercepts: Returns a matrix of intercepts, of dimension length(lam1s)xlength(lam2s)
coefficients: Returns an array of coefficients, of dimension length(lam1s)xlength(lam2s)xncol(x).
p1: p1 value used
p2: p2 value used
lam1s: lam1s used
lam2s: lam2s used

References

Witten, DM and Tibshirani, R (2008) Covariance-regularized regression and classification for high-dimensional problems. Journal of the Royal Statistical Society, Series B 71(3): 615-636.

Examples

Run this code

library(lars)
data(diabetes)
attach(diabetes)
scout.out <- scout(x2,y,p1=2,p2=1)
print(scout.out)
detach(diabetes)

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